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Math 250 Midterm #3. April 30, 2004
Attention! Please, note that this is the closed book test. You are not allowed to use graphing
calculator. Simple calculators are allowed. Please, show all important steps in you solution but do
not make your solution excessively long.
1. (15pt) Write the Lagrange equations, DO NOT SOLVE, for the problem of
finding the closest point to the origin on the surface
xyz + xy + yz + xz + 6 = 0.
2
2. (20pt) Change integration order in the iterated integral.
DO NOT EVALUATE:
1
2
2x
x2
tan(x + sin(1  y2
)) dy dx.
